Question

Assume you just deposited $1,000 into a bank account. The current real interest rate is 2%, and inflation is expected to be 6% over the next year. What nominal rate would you require from the bank over the next year? How much money will you have at the end of one year? If you are saving to buy a fancy bicycle that currently sells for $1,050, will you have enough to buy it?

Answer 1

Answer:

Part 1:

Nominal rate=8.12%

Part 2:

$FV=1000(1+0.0812)^1\\FV=\ 1,081.2$

$1,081.2 is the money you will have at the end of one year.

Part 3:

The Saving account is short of $31.8 ($1113-$1081.2) to buy the bicycle after 1 year because of inflation.

Explanation:

Real Interest rate=2%

Inflation rate=6%

Deposited amount=$1000

Part 1:

Formula:

Real interest rate=$\frac{1+Nominal\ rate}{1+inflation\ rate}-1$

$2\%=\frac{1+Nominal\ rate}{1+6\%} -1\\Nominal\ rate=[(0.02+1)*(1+0.06)]-1\\Nominal\ rate=0.0812$

Nominal rate=8.12%

Part 2:

How much money will you have at the end of one year can be calculated as:

$FV=PV(1+i)^n$

where:

FV is the future value

PV is the present value=$1000

i is the Nominal interest rate (Calculated above)=8.12%

n is the number of years=1 year

$FV=1000(1+0.0812)^1\\FV=\ 1,081.2$

$1,081.2 is the money you will have at the end of one year.

Part 3:

Calculating the price of bicycle after one year due to inflation:

$FV_{bicycle}=PV(1+inflation\ rate)^n\\FV_{bicycle}=1050(1+0.06)^1\\FV_{bicycle}=\ 1113$

The Saving account is short of $31.8 ($1113-$1081.2) to buy the bicycle after 1 year because of inflation.